Comparative Performance of Electrode Models for Thickness-Shear AT-Cut Quartz Resonators.

In this study, we compare four electrode models, i.e., solid model, added mass model, thin-film model, and a combining model of thin-film with added mass, for a 76.8 MHz AT-cut quartz resonator. Relative to the high-fidelity solid electrode benchmark, the combining model accurately captures the thickness-shear mode but overestimates displacement confinement due to mass loading and boundary effects. The thin-film model fails to replicate practical device states by ignoring mechanical mass and stiffness. In contrast, the added mass model optimally balances fidelity and efficiency, matching the benchmark's frequency and resistance predictions with a 43% reduction in computation time. Parametric studies further indicate that cut angle deviations (33°~37°) alter equivalent shear stiffness, while electrode mass variations (mass coefficient 0.99~1.02) modify vibrational inertia. Both of them are critical for frequency tuning. Our findings clarify the scope and limitations of these strategies, guiding high-precision simulations and designs for high-frequency resonators.